Question

Find the relation between x and y where point (x,y) is equidistant from (2,-4) and (2,-6).​

Answer 1

Let the points be P(x,y), A(6,-1) and B(2,3).
AP2 = (x-6)2 + (y+1)2
BP2 = (x-2)2 + (y-3)2
Given, 9(x,y) is equidistant from (6,-1) and (2,3)
(x-6)2 + (y+1)2 = (x-2)2 + (y-3)2
x2 - 12x + 36 + y2 + 2y + 1 = x2 - 4x + 4 + y2- 6y + 9
-12x + 36 + 2y + 1 = - 4x + 4 - 6y + 9
-8x + 8y = -24 
-x + y = -3
x - y = 3.